You’re neglecting the factor that the winner also gets to play again. So the payout at the end of the game becomes less important. I’d even argue that winner-takes-all actually has a counterbalance of making you care more about winning than the amount you win.
Now I haven’t done the expected return calculation that takes this into account. Maybe they still are too cautious. But I think you need to make the calculation entirely with your (2), factoring in the likelihood of getting the Daily Double correct.
The jump + low bet strategy is inherently conservative for (2), but that’s specifically because of (1) and (3). Because of those two factors, people don’t tend to play with the goal of maximizing payout.
Thanks, you’re certainly correct that the play-again factor must be considered in any analysis.
I’ll defer to the experts. The 2+2 author (Devin Shelly) concluded that most players “are far too risk averse” (on DD wagers), especially players in 1st or 3rd place. 2nd-place betting was more correct on average, but nevertheless deeply flawed because optimally, the 2nd-place position must adjust from aggression early to caution late.
Shelly advocates aggressive betting from the 1st place position because of the value of reaching Final Jeopardy with an insurmountable lead.
Now here’s the link again to the IBM research:
They analyzed wagers on the last daily double only. Quoting from the bottom of page 225: "… humans systematically wager these DDs far too conservatively.
“Leading players on average bet $2590, whereas the average recommended MC [Monte-Carlo] bet is $5380. For trailing players, the average bet is $3120 vs. an average recommended bet of $6970.”
Those are some stark differences, and the variations would probably increase (at least on a percentage basis) if all daily doubles were included because there’s less justification for caution early in the game.
Robot: I think it was his first day on the show; he hit a Daily Double, and when asked for his wager he just stood there. Alex (Trebek) had to press him again and ask for an amount. It sort of felt like Alex (Jacob) was stalling. I can see how that is a sound strategy if you’re in the lead, but as a viewer I don’t like it.
Rick Jay: The game is much more edited than you might think. If a contestant goes into the tank to an extent that’s problematic, they can just cut some of it out.
I noticed this same phenomenon on several occasions with this particular contestant and I feel certain he was “slow playing” with the lead, though I admit he was more than a little unconventional in his behavior.
I have long advocated for a requirement that all “answers” must be “questioned” in order to prevent this very “strategy” and also to prevent Alex from causing questions to be unanswered because of his frequent and unnecessary adlibs and particularly his pronunciation corrections during the rounds. Editing could easily satisfy any time problems.
Thanks for your observations. I don’t watch the show, but his behavior was probably “normal” for a poker player. My reaction would be that he should have done a better job of adjusting his ethical standards to the situation.